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Where are nature’s missing structures?

Abstract

Our society’s environmental and economic progress depends on the development of high-performance materials such as lightweight alloys, high-energy-density battery materials, recyclable motor vehicle and building components, and energy-efficient lighting. Meeting these needs requires us to understand the central role of crystal structure in a material’s properties. Despite more than 50 years of progress in first-principles calculations, it is still impossible in most materials to infer ground-state properties purely from a knowledge of their atomic components—a situation described as ‘scandalous’ in the well-known essay by Maddox1. Many methods attempt to predict crystal structures and compound stability, but here I take a different tack—to infer the existence of structures on the basis of combinatorics and geometric simplicity2. The method identifies ‘least random’ structures, for which the energy is an extremum (maximum or minimum). Although the key to the generic nature of the approach is energy minimization, the extrema are found in a chemistry-independent way.

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Figure 1: All 17 geometrically possible structures with four or fewer atoms per unit cell.
Figure 2: The average bond type for the L10 structure.
Figure 3: Deviations of bond averages.
Figure 4: Likelihood measures (total bond averages) for each compound, ranked in descending order.
Figure 5: Likelihood measures for b.c.c.-based structures with four atoms per cell or fewer.

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Acknowledgements

The author gratefully acknowledges financial support from the National Science Foundation through Grant Nos. DMR-0244183 and DMR-0650406. I would like to thank the following individuals for fruitful discussions: R. Drautz, S. Bärthlein, S. Müller, M. Leone and B. Kolb. Input from V. Blum was particularly useful.

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Correspondence to Gus L. W. Hart.

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Hart, G. Where are nature’s missing structures?. Nature Mater 6, 941–945 (2007). https://doi.org/10.1038/nmat2057

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